How many black holes can fit on the head of a pin?

Black holes are regions of space from which nothing can escape. If you consider a spherical object of mass M and radius R and set the escape velocity from the object to be ccc, the speed of light, you can determine a relationship between R and M, R=2GM/c2R=2 GM/c^2R=2GM/c2, where GGG is Newton's gravitational constant. This radius is called the Schwarzschild radius, denoted by RsR_sRs​. If mass M is concentrated into a region with a radius smaller than RsR_sRs​ then you have a black hole, and if not, there is no black hole.

From the above relation you can determine the minimum mass of a black hole, as roughly speaking the Schwarzschild radius must be larger or equal to the Compton wavelength - the minimum size of the region in which an object at rest can be localized.

Find the minimum mass of a black hole in μg\mu gμg.

Finally, a bonus thing to think about. What does this result mean for the masses of the particles that we see in nature?